I'm interested in this, though I know very little about it. Just an old retired school teacher.

The multiplicity formula doesn't make sense to me. Can you explain why it is?
It seems to me the part (a) is similar to the "how many difference license plate" questions we give in grade 12. How many different states for the first dipole x how many for the second, and so on so (2^10)^23. Yes, a HUGE number. I wonder if a calculator can show the answer? I hope you will post the awer so I can see it.

(b) and (c) boggle my mind! It could be changing to a microstate it had already been in previously, cutting down on the number "explored".